The solution of `xdy=(2y+2x^4+x^2)dx`, is (A) `y=x^4+xlogx+C` (B) `y=x^2+xlogx+C` (C) `y=x^4+x^2logx+C` (D) none of these

The solution of the equation xdy-ydx=sqrt(x^2-y^2)dx subject to the condition y(1)=0 is (A) y=xsin(logx) (B) y=x^2 sin(logx) (C) y=x^2(x-1) (D) none of these

The solution of (x^2+xy)dy=(x^2+y^2)dx is (A) logx=log(x-y)+y/x+C (B) logx=2log(x-y)+y/x+C (C) logx=log(x-y)+x/y+C (D) none of these

int[1/logx-1/(logx)^2]dx= (A) x/logx (B) xlogx (C) logx/x (D) none of these

The solution of y(2xy+e^x)dx-e^xdy=0 is (A) x^2+ye^(-x)=C (B) xy^2+e^(-x)=C (C) x/y+e^(-x)/x^2=C (D) x^2+e^x/y=C

The solution of cos(x+y)dy=dx is (A) y=cos^-1(y/x)+C (B) y=xsec(y/x)+C (C) y=tan((x+y)/2)+C (D) none of these

If the slope of tangent to a curve y=f(x) is maximum at x=1 and minimum at x=0 , then equation of the curve which also satisfies (d^3y)/dx^3=4x-3 , is (A) y=x^4/6-x^3/2+x^2/2+1 (B) y=x^4/4+x^3-x^2/3+1 (C) y=x^4/4-x^3/7+x^2/3+3 (D) none of these

The solution of the differential equation (dy/dx)^2-(xdy)/dx+y=0 is (A) y=2 (B) y=2x (C) y=2x-4 (D) y=2x^2-4

The solution of the equation dy/dx=x^3y^2+xy is (A) x^2y-2y+1=cye^(-x^2/2) (B) xy^2+2x-y=ce^(-y/2) (C) x^2y-2y+x=cxe^(-y/2) (D) none of these

The solution of dy/dx+(xy^2-x^2y^3)/(x^2y+2x^3y^2)=0 , is (A) log(y^2/x)-1/(xy)=C (B) log(x/y)+y^2/x=C (C) log(x^2y)+y^2/x=C (D) none of these

e^(dy//dx)=x A) y=xlog((x)/(e))+c B) y=xlogx+c C) y=e^(x)+c D) x=ylog(ex)+c